{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 1: Learning math with code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**NOTE:** Most of this code is not explained in the chapter. It's just here in case you are curious!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1 Solving lucrative problems with math and software"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1.1 Predicting financial market movements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "from math import sqrt, log"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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moTKk3QX4JjLfQAWBosxQDrhq6LT0RLn5ob286ydP5BWnPxaGMg05JSb6ogkqQn7WLajhlAXWYl9REuCNGxeybsHA4t9UXcr/vet0AB7d154eP94Xoz+WpCeayMhZGC8L68r59ls2sO1Ll3HdJStp642Oul6Qs39ZyE95yD9khrS7FWd7rwoCRVE8Zn+bFZmyqK6c5u4IX/3T89z3fAt/etabepDheGKQaag8GCCWsOzn4Vgi3T8g4LeWpoohykifu7KR6tIA/9hrCYJQwEdLT4TVX7gbgKoxxvqPxLwaK5eheZQalKMRhAI+KksC9A5hGnL7DgpR1iJfRhQEdoOZ14vIf4rI7SLyvyLyKRE5aSImqCiKNzhVNU9ZWMvulgFzx/Yj3Z5cL1ejmIoSa6HvjSToiybTn50GNKXBofsJNFaVEEukqAj5WTuvmr/tak1vqyygRuBmbq3lL3A/ueeDoxGUBPxUlgaGdBZ3T0VBICJfAv4OnAU8Dvw38CsgAdwkIveKyMleT1JRlMKw7VAnZ990P53hGPvb+miqKuHMZXUZ+xwbpo/weMhlGlpYVw7AC+19hGMD2bZBWyMYLkLnzadZVYlf/5IFVJcFM0pUF9JH4GZujZUHcHSU35HjBA75fVSVBnM6i5MpwwGXj8ArgZyLkTSCJ4wxLzHGfNwYc5sx5q/GmLuMMd8wxrwSuBoYf/qeoigTwnfu38Phzn4e3dvO/vY+ltRXcPUZi7nwxIEKv07t/0LTa/sA3JxoF3XbdazH3m4t4OedYPURmFeTGbHj5l3nLOW295zB516xZpApyDPTkK0RbD3YOarj0hpB0EdVSYDeLGdxKmW49Bt/40ePvADAazfM55dPHJywyKFhBYEx5o8jbG8xxmwu7JQURfEKZyEOx5Lsbw+zuN56Ip/lSppq9iCUNJpI0h1JZOQFgKURlAZ97GrusU1H1vzec+4yHv7Uhay0BUUufD7hpcsbCPp9gzSAbF9EoSgPBbhq/TxufXT/qEw3jiAI+X1UlPh58sVO/rG3Lb39aHcko1PbOSsb6I8nR615jJV8fAQniUij/b5eRH4kIr8QkanVWUFRlBEpt00vx8MxWnuiLJhlCQJnAQ74hBfa+njJl+9lT0tPwa7bZkfAONU8Hfw+YVlDJfva+jIKsYlI2myUD9mCoCTgXRzM5WvnYkxuE9pDu1q5a9uRQePRtEbg59nDlsnnc3c8m96eHU7q5C6M1ik9VvL5tn7gev8V4BhwB/BjT2akKIpnOF3BdjdbzmHH+XnhiU0AXL52DmDF5N++5VDBrusUWcsWBADzZ5Vx+Hh/hkYwWpyKoOesaODma17CKQtrxz7ZEWissrSnXBrB23+8iQ/e9tSg8ahLI3jFKXMBaHB9F04fZwentMaUEAQi8kWsjmLvt9+/BvADq4AFIvIFu/2koijTAMf3+szhLsAKhwS4ePVsnvr8pXz44pXpfeOJwuUTDCsIasvY2dxDImWYP8ZCcY5GUBr087KT5ox9onlQX2Hdw3Bx/tl1k9LO4oCP6y9fxcWrmjIESXf/5GoEw7rWjTE3iMhVwG3AHOA8Y8ynAUTkEmPMjRMwR0VRCkS/XeDtuaOWecLRCMDyE7j7/I4lg3YohhME81xzOHv52JrNO4LAPwGZUU6Pgva+TI0g6Ypw2tfal5EENxA+6kNEWNpQwd/3tmGMQUToiWYKgsqSAOUhvyf+mlzk87XdCDwE/Az4HFh+A6BtuIMURZl6hLMKuzkagYOI8OAnLuCsZfXs80AQOE/Tbty1fBzn9WgJ+KylzF+gQnPDUVkSIBTw0d4b4+t3P89rvvd3eiJxWnoGnt53Z/lXoi5BAFaTnUg8lS4j4TYNvXR5PSLC7OrSqaERABhj7sDyCbjHtmOZiRRFmSb0RRPscxVMqyoJDIrrB1jSUMGGRbU8sb+DVMoUpIpnZ3+MqlJrAc3mpHnWk/PXX3dyumHNaEkZ62ncN8bjR4OI0FARorU3ym+ftKq27jjak6GN7GnJFKLuhDIYEH4tPVHqK0vSzuJnvvSydMRTbXmQrv6xt8YcDSP5CJaMsF1EZMEQ20pFZJOIPC0i20XkBnv8ZyKyU0SeFZEfi4g3Ab9DcKC9jx8+tI9rbnncs5oqijIVufpHj6d9AwB1lUOnAM2tKSWRMnz89qf5/oN7x33t7v7EkC0eVzRV8tyNl/HG0xaO+fyL7AijjYtnjfkco6GxqoRDxwfyLQ52hDnYMfB5d5YgcJeYAKgps74LJ8O4O5KgNGglmznlNapLJ04QjKQR/LuI+IA7gS1AK1CK5UC+ELgY+CKQK7wgClxkjOm1F/tHROTPWCamt9n73Aa8G/j+eG8kX87/9wfT7w90hFnaUDFRl1aUSSU7CWq4Vo5zbJPRHU8dZnljBe+/YPm4rt0diQ+b7ZtdemK0bFg0i79+7DyWN05MG/SlDRX85bnm9Ocv/n47V6ydgwhcdGITe4fQCBxBUF1m3a/jJO6JxAclwdWUBdNlQLxmpISyNwCfB04Evgs8jCUU3g3sxFro7x3iWGOMcb6NoP0yxpg/2dsMsAnIqVFMBNuPdI28k6IUKcMlXc11ZfS+0NY37gzX7v441WXeKv8rmqrGbFoa/bUqM/wtvdEEt285xLyaMk6aX8P+9r6M3IBoIknAJ2kfhqMddUfitPZE+fmmg1Rl9V6oKQsOiibyihGdxcaY54wxnzXGXGCMOdEYs8EY81ZjzE+NMcN6MkTELyJbgRbgXmPM465tQeAa4O7x3kS+GJNpCnISOxSlWGntibJ5fwe/euLgoG3DrZlzbEEQ9AspQ7pR/FjpjgxtGpqOrGjKnfF8uLOf81Y2kDJw//Mt6fFYIpXhH3GEYld/nL/vseJu3FFG1j4BuiOJQeuWF3gabGWMSRpj1mM99Z8uImtdm78HPGSMeTjXsSJyrYhsFpHNra2tuXYZNe1ZjR42vdA+oc0fFGWiedPNj/L6HzzKp36zbdC24QRBXXmI05fWcd0lVmvIHUfH99BkaQTeFIKbDNwm5S9ftZb7P34+AG85fRGnLprFrPJgeoEHq1WlO9vZMZN19yfSkUFfec26jGvUlAVJpkzOFp6FZkL6ERhjOoEHgcshnajWCHxsmGNuNsZsNMZsbGxsHGq3UeGUjr3+ilW87tQFPPliJy/515yWLUUpCtxRQq/ZMD9jmzC0JPD5hF+99yzef/5yykN+rv/tMzy4s2XI/d0YY9LtJx26I/Gi0gjcDe1XNFayrLGS7TdcxpdffRI+n1BfWZLRc6CrP55higv6fZSH/HRH4jR3R6kI+Qe15axxaQ1e45kgEJFGEam135cBlwDPi8i7gcuAtxhjJrRLs1PA6ZwVDekogwnQuhRl0igNWj/xN21cyDfftJ73nLs0nT2czxO6zydpW/gXf789r2v+fNNBVn/hbg52hPn3e55ny4EOeqMJz30EE4k78c7poVBREkhH/Lh7MRtj+MfedjZkRTQ5PoDm7sigvsjg8iNMgCDIS1cTywNzNbDMGHOjiCwC5hhjNg1z2FzgVhHxYwmcXxlj7hKRBHAAeNR27Px2ojKUHclaUxbkqg3z+OZfd03EZRVlUuiPJYnEU1x9xiK++Eqrj9RnX74mnQH79rMW53Wey0+aw93bj7FqztCVQN384Wmr6Nq5X38AgKde7MQYCto+crIJupIGckU8lQUHWnA+f6yH1p4oF5yQadmoLg3SHYnT3hvLKQgmUiPI93/me0AKuAgr07gH+A1w2lAHGGO2ARtyjE/aX4PTJ7S6NEhNeZD3X7CcHz60L53mrSjFxC2P7APg9KV1GY5Kv0/42KUn5H2eb7zpFDZ/vYNEMj/1OVvTcGzgxWQacpOrUF5pyJ9ewB1H+/qsQnjVZQE6w3GaeyK8ZNHg/IeGqhJOmled7tbmJfkuymcYY04VkacAjDHHRWTaNaRxkjccVa6yJEAiZYgmUsO2xFOU6YhTPfSMpfXjOk95KMDKpiq6I/k9mTr1cU5fUkdNeZB77Xj7sZaPmOpU5NQIfDR3Jdl6sJPrfrkVgEVZ9z+3pownXzxOZzie0Q/C4YTZVfzxw+d6M+ks8vURxG0TjwHL/o+lIUwreiJxykP+QY2xs+uvKEox0BmO846zFqdDQcdDdVlgUKnkoTjYEeZNGxfy82vPZH7tQC2jVXOqxz2PqUiuMh2Oaej7D+5JjznlJRwW15dzuLOf3mhiUA7BRJOvIPg2Vr2hJhH5CvAI8FXPZuURvdFEhmfeadKRXTJWUaY7qZShOxKnZpjs4dHg2LNHoqMvRntfjKWNFfh9kq4sWlUaoKa8OE1DueonlYUsQbCk3gozze7MBrC4viIdrFI5yf6TvASBMeZnwKeAfwOOAlcZY273cmJe0BNJZKS5O0KhVwXBjOOxfe1F/f/eE0lgzIDDcbxUZ2W5GmMyyi6DVYb583daXbc22PbwdfNrEYHXnTppBQQ849I1s4fcVhr0E4kl0w7jP3zo7EH7uE1lFZOsEeQbNXQmsN0Y8137c5WInOHOFJ7KJJIpvn7PTna39FBZ6g77sm4/HCveBUEZTGc4xptvfoyLVjXx4/9vyHiHaU1nv5UoWVsgQVBTFqQvliSeTBH0+/j0b5/hwZ2t/OP6i9LVSZ968Th/3HYUgJMXWILgrOX17P3KlQWpYDrV+P7VpxIfwoHumIZ6IwkW1pUxt2Zww50FriY82TkEE02+pqHvA+4qSn1MYKG48bKzuYebH9rHrubejBA2x0fQG1UfwUwiErfcW88eLt5aU07ESm2BzDHO78YJuPjFEwc51h3htd//R7oEQmfYuuY5Kxoy7ObFKAQAAn5fTv8AWIIgkTIcD8eoLMn9f+BOShuuIN9EkK8gEOMqeGEngk2boGC3Mzjkiv9NawRFbCJQBuO0DUwVMJvw4d2tOZuZTxbOolxI0xAMJDc5nca2HuxMCx2ny9aNrz6pINeczjgCorU3OqQj2O08zhV5NJHkKwj2iciHRSRovz4C7PNyYoXEXQXw8Rc60u/VRzAzcey2hWpHkUoZrrllE6//wT8Kc8IC0FlwjWCgWmYimaK9N5qut+P03nW0hexyyjMRJxy9tSealyN4WjiLgfcBLwUOY/UeOAO41qtJFRrnDxTg4y8bSKRxEkE0amhm4aT+F0ojcBZdp1HJM4e6WPele2iZoDaDuXCe0gtV1mFAI0jQ2hslZeCkeVY4aGuP5Y8YEATTxljgGWVuQZCH/X9a+AiMMS3GmDcbY5qMMbPtMtT5VaCaAjjq7KbPXsw/nb00Pe6Yhiaiup8y+ew81kM8mUprBNlRL2OlvTezwfjND++jJ5Lg4d2T19a7rSeKyPDNZ0ZDupFKJJ42ga2db5VNdjSC7kickN+nyZkMmIZSJr+n/ckWBMNeXUQ+ZYz5uoh8BzuZzI0x5sOezayAdLtKS7gpCfgI+EQ1ghnAoeNhLvvWQ7z7nKW8dIWVaVuoVqVtvdYTsVMKIJGc/FzLo139NFWVZNTEGQ/uAmhOc5U1cy2NwG0aUm3Awl1pNJ9ksck2DY109R32v5u9noiX9EQSBP2SUQ8crCbU5SG/CoIZgFN59u9729lg13XpiyU5dDzMglnjK33gLIRBv487tx5Om0ja+6LDHeYpR7si6XaThSBtGooMCILF9eX4fUJrT5TuSJyu/uHbUc4k3PWHhnvav3TNbO59rnlQ1vFEM+z/mjHmD3ZpibXGmE9O0JwKjtMPNFdhucqSgJqGipxUyqS7RQkDzmKAc772APtvevm4zu+YhvrjST7yi63p8daeyRMEx7oiBe3fWxHy4xPL9+D3WQ9UtWUhmqpK+N6De/me3eB+3fya4U4zY3A7zId72v/uW0/Nu4aTl+TTqjIJvGQC5uIZw6msFSUB1QiKnF9vOcT37YUKMgVBIcjufOfQMsmCoBA1hhxExM4uTqR9bpWlAb74yjUZ+6lGYOH+HoYL4Q0FfDnLT0w0+f6vPSUivwdux0omA8AY81tPZlVgLI0g962Wq0ZQ9OxtG8iF7OqPE8nz//umPz/PGcvquPDEpmH3Ox7OLQieOdSVzsSdSHoicXqiiYwG9IWgpsyqNxT0+6gsCeD3CZevnZuxT7HxVyIiAAAgAElEQVSWmh4t7mitQuVyeEm+f6F1QDtWP4JX2q9XeDWpQtMRjlNbljt6orJEfQTFTmffgOp9rDtCWx62+1gixQ/+tpd/+p8nRtw3nCMz/eQFNexr6+NPzxwd3WQLgFP/v5AaAdiF5/rjdtvJgQeruz50Tvr94obiLDU9Wtx+gWISBJ80xvxT1uudns6sgBzsCLOwLrfjrCKkpqFi50BHH/Nry/jmm04hmTLc8eThEY85dDyc9/lzmZr+4w2nANDem1tb8BLHMZ6rvs14qC0P0tEXS/vcHNbOr+HkBZZv4MTZ+XUxK3b8rrIa014QiMgrRaQV2CYih0TkpRM0r4LRHYnT0RdjsV0ONpuKkgB9WnSuqDnY0c/pS+u4av185teWZdjunZ6+2aGk+9stC2hdjoYh2WT3s3jzaQvTBcVikxBKOiAICqsRLJhVxuHOfrr7E4O6kDkJbCubVBBkM+0FAfAV4FxjzDzgdVhlqKcNxhgu/cbfAFgyRHekihI/fVp0rmgxxtDcHWFuTSkikn5ynV1dwnWXrCQST/HuW59g/Y1/yShFsr/N0giaqkZ25PXHkukChgA3ve7kdE2rWGLiBYGT8NVUXVgn5IJZ5bT1xmjuiQwqI/GFV6xhUV05K2cXLlKpWChUdreXjCQIEsaY5wHsktN5i3sRKRWRTSLytIhsF5Eb7PGlIvK4iOwWkV962fKypSeabpu3qG5ojUBrDRUv3f0JEilDvR2ZsdpOgkqmBuy4f93RQnckwZHOgZIQx2w7ez5ZsuF4glOy+tEG/D58MjmC4GhXhIbKUMFj0x0tZ19r36BG9Bevns1Dn7pQs4pzMB2+k5GihppE5GNDfTbGfGOYY6PARcaYXhEJAo+IyJ+BjwHfNMb8QkR+ALwLj0paP3e0G4Ar1s5h9dzcMqwiFCCWSE1KdIfiPY5juKHSet5wGoifvaJ+UCSZlQBm/Z04PSr684gwCseSLM7xoBEK+CbFNNTSHaGxqrBmIcisn19boNIVytRgJEHwQzK1gOzPQ2KXrXbi9oL2y2BFHr3VHr8V+BIeCYLnj/YAcNNrT86ZTAYDNuDWnijzagvrXFMmH8dZW19haQTnrmzgDx88h5PmVfPnZ4/l3BcG7P7h+MjaYiSWpCzk59Z3no77r6wk4Cda4JyFfGjvi6UFXyFZ0Tjw0z9zWV3Bz19snLOigcf2tU/2NPJipMziG8ZzcjsreQuwAvgusBfoNMY4v65DwPwhjr0Wu8LpokWLxnT95u4I82vLhu2VuqzRepLb29qrgqAIcbJ+6+2FUURYZ/sJsjWCDldimKMJuENDUynDF3+/nbecvog18wYasYfjScpDfs4/oTHjfJOlERwPx1hUV/gwzpryIGvnV/Ps4W7OXtFQ8PMXGz999xmYAva88BJPbSHGmKQxZj2wADgdWJ1rtyGOvdkYs9EYs7GxsTHXLiPypVedxP2fOH/YfVY0Wc6tPS29w+6nTE/a7MW9PscTcnZEkDtDOK0RuExDhzv7+b/HDvD+n23JOC5sawTZhPw+ohPkI2jujnCwI4wxho7eWF7RTmPhZ+8+k7s+dI72HMiToSwRU40JyQc3xnSKyIPAmUCtiARsrWABcMTLa4/kMGusLKG6NKCCoEhps0NF63LYtJ2HALAq0Xa4Es2c3ID+eJJUyuDzSbq4nPunnUwZYolURrVJ9zknyll8xlfvA6wop55ognqPBEFNWZAarSdUdOSlEYjIoDg0ERnWSCgijSJSa78vAy7Bqmb6APB6e7d3AHeOZsKFRkRYVF/Okc7+yZyG4hHtfVFmlQcJ5AgEcEdzLJhVxqYXOrjb9hu4ncQ7jnXzv4/uT0egOQ8X/bEk92y39i/PpRFMoCBwcHIk6jzwESjFS76mod/akT8AiMhc4N4RjpkLPCAi24AngHuNMXcB/wJ8TET2APXALaOfdmGprygZsnCYMr1p742lQ0dzsWqO5QCdU1PKruZe3vfTLRhj0lFDAC//9iN84c7t7Gmxgg9Cdjnzj/5yK//8sycBKMvRc3ayfASQWwNSlKHI1zT0O+B2EXkdsBD4PfCJ4Q4wxmwDNuQY34flL5gyNFSWsLu5Z7KnoXhAe29sWDPJHf98NpF4kq/d/TxWOS2r0UyusNGtBzsBcMy+d28fiDoqz2EaCvknXiNwGE74KUo2eQkCY8wP7cSv3wFLgPcaY6ZOp+5x0lAVoq0vhjFm2jh3lPxo64uyek71kNvLQn7KQv6MGPl7n2vmSFeEipA/ozLtUy9agqAzHB8UDTKZpiF3eYxPX7GKly5vYO38oe9ZUbIZqdbQx5wXUIqlDWwFzsxKNJvWNFSUEEukOPfrD0z2VJQCY5mGRjaTNLkSsD5zxzMAvGHjQk5fOuAKc8yHx8OxQdFAuZ7AJ8o01GNnxn/4ohVce94y1i2o0QcaZVSM5COocr0qgTuAPa6xoqChylooDh3vnzZxv8rIxBIpuvrj6WSy4cguogZWhMy15y4bNN4TSaSLrDnkqkk0UaahrrA1l0X1FSoAlDHhaULZdMFpvQfQG01ojHSR4DSMyUcjuHTNHL7wijXc/3wL+1p7OdIVwRhDY9YCf8bSOh5/oYOnXjyeMZ6rwNtEmYY6+637rJ0Gxc2UqUm+4aP3OqGg9udZInKPd9OaWC47aTbL7QzjyWwvqBQWp6dAPuWY/T7hnecs5afvPoP3XbAcgNbeGOvm1/Chi1bw2StXUxHyc90lJwBwz/bmjOPLc0QNlQT8Y0ooi8STI2qmLd0RInaug1Mao3aYDHpFGY58w0cbjTGdzgdjzHFg+P5904iSgJ8vv3otAC3dKgiKhb0tVk8Bd+JYPjjlGYJ+wecTPv6yE3nPect49obLOGt5PcsaK7hvR/MIZxmbj6C9N8qqz9/Njx5+Ych9UinD6V+9jw///Cl+9vgB/uknT1BTFhz1fSqKQ76CICki6YI/IrKYIUpDTFeaqq2nxl3NPRl16ZXpy97WXkJ+Hwtmja7uzvknNPKV16zlk5edmDHu2N9Pnl9Dd2TkYnRjySx2msr85slDQ+9jl8j+y3PNPPFCBwA3X/MSrQiqjJl8BcFnscpI/5+I/B/wEPBp76Y18Tg23i/+fjvrvvSXvMoPK1Obva29LG2oyGgbmA8iwtVnLB7SV+QuOPfJy07kp+86I+d+XvkIDrT1pd+/2BHmrGX1nLGsvuDXUWYOeQkCY8zdwKnAL+3XS4wxReMjAKgqCRD0DywY5379/kmcjVIIOsPxdERYIVkzd6DWzlUb5nPOytyVOEP+0ZuGnP2HcxG8YLfRDPqFFzv6Pak0qswsRlN99KXABfbrTC8mM5mICNWuJ8C23piGkk5zvGo25JQuB6jM4SR2KA36SKYM0UT+2qWjiZphLK8H2i0neDxpaOuNsmiINqyKki/5Rg3dBHwEeM5+fUREplX/4nxw6tMHbFNCJD455QGUwhBLGk8EwZzqgSikipKhq9vW2fkLx/vy9zk5Za+HewY5nFUgcaFqBMo4yfdXciVwqTHmx8aYHwOXAy/3blqTg1Oh0ik30K1O42lNPJlKN5EvJD6XzyFXVVMHJ3/BKV89En/b1cp7/nczMHwkhtOc3kFNQ8p4Gc2vxN2duygLkjs/byfKpLtfBcF0xjINTV6mbcMoBcEfnh5ozTGcWfJYV4QNiwZ+jioIlPGSb/XRfwOeEpEHsNbL84DPeDarScLJzleNoDiIJ7zxEQB8/+pT2XFs+Iq1DXb9IXcv5OEIZEU3/e6pwxzp6uefL1iRHkumDM3dEV5xytx0EbxZmkimjJN8q4/+3O4wdhqWIPgXY8yx4Y+avsy3exdn15NRphexpCEY8EYQXLFuLlesmzvsPk4hurbeKMe6IjRUhoY1JbnDXI2B6365FSBDELT1RkmkDAtduRFaX0gZL3kJAhG5zxhzMVYfguyxomNBna0R9I+cNKRMXbzyEeRLRchPadDH/vYwZ/7bfVxz5mK+fNXaIfd3awT7XLkCXeE4NfZT//O2FrK4vpzvXX3qsE5lRcmXkcpQl9otKRvs+kJ19msJMG8iJjiRiO0laKy0okLUNDQ57G3t5dO/3UZinCWcJ9tHICLMqynjyQNWgbp7th8jEk/SGc5tKoqncq/qTt4AwAPPt1Aa9HHakjquXDeXl588vFaiKPkw0uPSe4EtwCr7X+d1J/Bdb6c28Vyxbg4wECeuzuLJ4UO3PcXPNx1kV3PvuM7jVR7BaLh0zWx22t3vUgZe+71/sP7G3F1e+6K5NdD9Lu1g84EOTltSl9FvWVHGy7C/EmPMfxpjlgKfMMYsM8YstV+nGGP+a7hjRWShiDwgIjtEZLuIfMQeXy8ij4nIVhHZLCJTpm3lhy9ayZOfv5R5tWVUlQbSzcqVicXxzQz15JwPxhjiHuURjIbzT2hMvzfG8NzRbgBu33xwUHvUnqz6RQ2VJVSVBHhgZwvxZIrTv/JXnj3cndFNTVEKwUimodNEZI4x5jv257eLyJ0i8m3bZDQcCeDjxpjVWJnIHxCRNcDXgRuMMeuBL9ifpwQ+n1Bn97dd0VTJnpbxPZEqY6PfLq98zC6u9uzhLp7Y3zGqc8STlpkl5JGzOF/qXL0QUi6D/id/vY3P/u7ZjH17swSBT+D1Gxfwx21HeWxfe7pEurubmqIUgpF+Jf8NxABE5DzgJuB/gS7g5uEONMYcNcY8ab/vAXYA87FyZZyqXTXAkdxnmFxWNlXy6L52/r6nbbKnMuMIx6wF0REE7/jxJt7wg0dHJQzitn8hOyRzoqktcwuCzG3tvVEOHQ+ny0o4PqlPvOwEvvqadXzv6lM5Z0UDiZThJ3/fnz5udrUKAqWwjCQI/MYY59f3JuBmY8xvjDGfB1YMc1wGtnN5A/A4cB3w7yJyEPgPhqhiKiLX2qajza2trfleqmA4STpX/+jxCb/2TCaWSKVLezR3RYgmkulewU8f7Bzu0AwStkYw2aYhd7OYVJYk2Nvaxzlfe4Av3GlpBr3RBK/dMJ8PXrSSt56xiI1L6lg913pmuu/5lvRxudpiKsp4GFEQiIgTYnox4C7JmW/oaSXwG+A6Y0w38H7go8aYhcBHgVtyHWeMudkYs9EYs7GxsTHXLp5y1Yb5AINaFSreEnEVaDvWHWG3y2Hc3B3JdUhOnCqeXuUR5IvbqZsaItZz84HjGGPoDMepzmo3ObemlOrSzJ+a/k0qhWakX8nPgb+JyJ1AP/AwgIiswDIPDYuIBLGEwM+MMb+1h98BOO9vB6aMs9jNglnlvP2sxWkTQyKZ4uO/epr/uGfnJM+suIm6Cv2198bY6crePTYK573z/xaaxPDRbIYKDxWB4+E4vdHEIEewiHDinKqMsTl5tN5UlNEwUtTQV4CPAz8BzjEDBVB8wIeGO1asdMdbgB3GmG+4Nh0BzrffXwTsHv20J4ZZ5SG6+uMkkimOdkX4zZOH+K8H9qRt2ErhcfrwArT3xTh4PIwIbFhUS3NX/hqBIwgm2zTkZqgmNfta+/iv+/cAsLi+YtD2pQ3W2LXnLePxz1ysPgKl4Ixo3jHGPJZjbFce5z4buAZ4RkS22mOfAd4D/KdtcooA1+Y/3YmlriKEMfDUwU4qSwa+qjVfuId7rjtv0JOaMn6cZu+zyoO2M7Wf2VWlLJxVzlMHj+d9nqkoCIbjx3+3ehTnKiDnlLOuCAVUCCie4NmvxBjziDFGjDEnG2PW268/2eMvsXMRzjDGbPFqDuNllh1K+oYfPDooxvuxfe2TMaWix2niMq+2jO5Igl9vOcS82lJmV5fQMgrTUCwxNZzF1hxym6feesYiNn3mYt7wkgXpsVyCQIvKKV4z+b+SKUydqxn47pbM5J+SSXZCFitOxNC82gFb+Ysd/dSUBYkmUnl3+0r7CAKT7yN47NMX88AnLsgY+9zLV/PV16yjqbqUt5+1BIATZ1dRFhqcMfy2Mxfz9rMW8/+dvcT7ySozknzLUM9I3D/KZw9n+sbD2tzeE5yFfr5LEFx73tJ09E1PJEFJZe7yCn99rpkP3PYkWz5/6ZQyDdVXllBfWcJrT53PrPIQn3/Fmozta+dX872rT+XcIXofV5QEuPHVQxerU5TxMvm/kinMuvk1XLK6CYBnD3dnbBtP+QNlaJyooZKg9ad50aomrj1vebqNaLaJzs2/37OTaCLFgfa+gfDRKSAIHL7xxvWDhABYkUFXrptLVamagJTJYer8SqYgoYCPH759I9WlAZ7J0giOh7UgnRc4GsElq2dzyeombnjVSQBUlViLZM8wFWETKWvxjydNusTEVBIEijJV0V/JCIgI57oKh9XbDuR9bb0kh4gLV8aO4yOorwjxo3eclm7M7mgE3f0JWrojOb/7hD3W1R8nnnDyCPRPXFFGQn8leXDxqqb0+82fu4S6ihB/39PO/9ghf0rhcDSCkqwyy47ZZNP+Dk7/6n3ctunFQcc6ZSW6++MDPoIp4CxWlKmOCoI8cOq9gKUhdNi1b/a2anXSQuNoBKVZUVnVZZZG8IMH9wLwQmsf2TiLf1d/fEr6CBRlqqK/kjxYkpXt+d/XvASAGldlyUJx97NH+eBtTxb8vNOFkTQCZ4HPtb67TUPH7Cxkx5SnKMrQqCDIg+zY7stOmkNteZB+D0pNvO+nT3LXtqMFP+90YSiNwJ3ZDdCZ5aw3xtBrd/jqjsTZeayH2dUl1JarIFCUkVBBMEbKg376PMwliI+zX+90JZpI4vcJgaxHfr9PMoTBse4ItzzyQvp76o0m0rV8uvvj7Gzu4YTZWgJEUfJBE8ry5InPXpIRqVJeEvC0+Fwknpxx9u223ijffWDvkNtryoLpp/6Hd7fx8O42GipDvHr9fNp7B/I6Ovpi7G7p5R1nLfZ8zopSDMyslWYcNFaVZJT/rQj5Pc0ujsSLVyPYcbSb1Z+/e1Ar0E0vDN+BLFcdfkcLcJrXADz1YiexRIoT51QP2l9RlMGoIBgjZSE/4ah3giDfmjqFJhJPem6W+tuuVvrjSb59X2YF8iH6tqRZO99a2Oe4KnC22ZpAe69VkG5hXVm6t++JahpSlLxQQTBGKkIB+jw1DU2ORrDq83dz9Q+9bc/pJIdlV3B1evb+4G2n5jzuM1eu5oZXncTquQMLvNO1zAnpXW1rAT6BlbMrCztxRSlS1EcwRiwfgZemockrardpFE3ix4KjSXX2Z0b+dNufz12ZuzVpeSjAO166hPULa1lcX8GDO1v4yT/289i+di5fOweAVXOq+MtzzSypr8hoE6koytCoIBgjlo+gsBqBcdlGJss0NBE4mpTVqD6ZUVnU7xPKc5RidnPKwlpOWVjLkuv3A/D8sR6WNlRQWRJggV2SQpsGKUr+qGlojHjhI4i6WhlOhmkoNUG1k9yalLvZTHckTnVpAKvL6chcf8Wq9PvnjnbTVFWSdihr6Kii5I8KgjHi+AjMSB7OUfDo3gGb+WRoBP0uc1Qh7yubvuiAJnW0qz/9vrs/PqpSzO87fzm3v+8sAA60h1nWWMnS+op0j2NFUfLDM0EgIgtF5AER2SEi20XkI65tHxKRnfb4172ag5eUl/hJmcyn+PHy5bueS79v741NeM8DtyDo7vfOEe7WCI51DzSk744k0jWF8mWWK3N4RVMlSxoqeORfLuL8E3L7GRRFGYyXGkEC+LgxZjVwJvABEVkjIhcCrwZONsacBPyHh3PwDOfJtTsSZ9MLHQVZtEUg4LPMIp/89TbeMkL0zqHj4QwtYrz0uxbo1t78+wOPlr5ogoV1Vgeyo10DgqCrP071KJuz1LlqCS1vtGpCza8ty9u8pCiKt83rjxpjnrTf9wA7gPnA+4GbjDFRe1uLV3Pwkpoya8F6eFcbb/zvR3n5tx8Zd3+CvmiSs5bXpz/vONrNK7/zyJBmmpd/+xHe8sPHCmbGcWsEbpNNoQnHkjRVlVJVEkgXh3twZwtbDhxPf6/54t5/zTxNIFOUsTAhPgIRWQJsAB4HTgDOFZHHReRvInLaEMdcKyKbRWRza2vrRExzVNTaC9D3HtwDwOHOfrYcOD6uc/ZE4oOyZ5853DWk+anLDrfs6CuMCcltstnb4l2J7d5ogvKQnzk1pWmB87idVfyBC1eM6lx+38CT/2rNJFaUMeG5IBCRSuA3wHXGmG6skNVZWOaiTwK/khx6vDHmZmPMRmPMxsbGqWfvdZ5E97b2sWpOFQGfcN+O5jGfL5ky9MWSGYLgnWcvBawF+vlj3UM6kA8eH//T+48feYGb/rwj/fme7c2eOazDsQQVoQBzakrTGkFzV4T5tWWsnV8zpnPWVYTw+dQcpChjwVNBICJBLCHwM2PMb+3hQ8BvjcUmIAU0eDkPL3CbJFbNqWLNvGqeO9o9zBHD4xRTa6wcEASr7Aza5u4Il3/rYT5x+7acxx46Hh7zdR1uvOs5Hts3kEj26L52bv3H/nGfNxd90STlJX7m1pSmfQRHuyLMddVyGg1bPncJf/vkBQWcoaLMLLyMGhLgFmCHMeYbrk2/Ay6y9zkBCAFtXs3DK9yCYMGscmrKgvRExh5p4zRldztLncSqI53WE/8fnj6S3ub2C7zYMX5B4OaNGxcAsPVgZ0HP69AbdTSCMlp7o8STKY51R5g9RkFQX1kyqrBTRVEy8VIjOBu4BrhIRLbaryuBHwPLRORZ4BfAO4yXQeseUe0SBPNnlVFdFkzXyhkLjhBx6vDUlAWpCFnv3SGWDu7wzq0vjm/Bfnh3pg/mQxet5IITG9mXox3keInEk3T1x2mqKmFuTSnGWBrP0a5+5laPTRAoijI+PCsxYYx5BBjKaPs2r647UbidlIvrytlWGhizRvDt+3bzjXt3AVZY6u8+cDbzakvTfXmbXSGWiWSKHUd70sKhIuTn0b3txJOpMfUvMMZwzS2bMsbKQn5Wzanm73vaxnzeoXCKxM2pKU37QzbvP04knmLBrLKCXUdRlPzRzOICcPrSOqpLg+miaaPFEQIAlaUB1i+spamqlPIcGsGOoz288r8e4T3/u5l5NaVcf+VqeqIJnj3cNaZrHw8PnnNZ0M+82lLiSTOoJeR4cXwC82rLmFtjLfy3ProfgAtXNRX0Woqi5IcKgnHwg7edyq/eexYBv4+q0gDRRGrUkTY9Weak6tIBJa28xPIRHHPV4/n1loPp9684ZR4vWzMbYMyhq47/wU1Z0J82UWXPb7w4UUJzakrTjX6eerGTVXOqWFxfUdBrKYqSHyoIxsHla+dy+tI6YMBnMJx5yBjDD/62l4Mu5252l65FdvVMGHAWu01Ddzx1OP3+xNlVzK4uZcGsMp58cWyC4HAOQeDzCVUl1v30RgtbasLRbuZUl1JdGsCxsJ27ctoFjilK0aCCoEA4T9Dd/fFBmb6Hjof53VOHae6OctOfn+cd/zNgk2/tySzl4G7anss01O0SNMubrMYryxorOdw52KGcD0ezBIFT4mJAIyisINjb0kt9RYiKEqvK6BlLrUzqoXoQKIriPdqPoEA4YZ89kQSXf+thmqpL+L93nQHA22/ZxL62vnSlTHc0jtNq8eQFNbz73GUZ53Q0gq7+OOUhPwL0xZIsa6zgpcvrWWuXVKgqDYw5l+BIV6YAcRy4Ven7Kaxp6KmDnaxfOFAZ9CfvPI2nD3Zx2pJZBb2Ooij5o4KgQDimodaeKDube9jZ3JPedtBepJ85NNih22YXd7v9fWdREshsyBL0+wj5fcSSKapLg1SVBtjd0ssZS+v516vWDVy7NDjmaqHZpqG3nbkYcGk4BdQIuiNx9rT08upT5qXHSgL+tHlNUZTJQQVBgXDKId/73OAyE36fEE8anj0yIAieOdTFugU1tPVGqS4NDBICDuUlfmLhFLXlQZbUV7C7pZemrHpE1WWBMecwHOns5+wV9XzvrS8BGXBWF9o0dKC9j3/6yRMArNSmMYoypVAfQYGYX2uFQj5kJ2e5qycFfNbX7IR4BnzC/z22n1TK8MzhLhqyFnY3TnG7UxfPoqHKEjYVJZlCo7o0mG77OFqOdPYzr6aMmvIgNWXBdPnmypLCRg3d+Ifn0iaxpuqh71dRlIlHBUGBKAv5aagMpePkS11P+E7y2a7mXipLAqxbUMPRrgh3Pn2Yp17sHLblpVOWev3CWpbY4ZW+rBp9zlP8jXc9xwduezKvxfuR3W1sOXCclp4o82oHJ3IF/D7KQ356bY0glTIZrSyP98VGVf464B+Ys7uekqIok4+ahgrIglnlaedvNJHEGIMxma0ZGypD1JWHONYd4bBdNfSjl64c8pzXX7GahsoSXnnyPPw+IZkyaTu+g+PYve3xFwE4c2kd15y1JOf5IvEkH7/9af647Wh6bF5t7tIO4ViSHz3yAu89fzlX/OfDNFaV8OePnMsLbX1c+B8P8uWr1nJN1lzcPHu4i2/ft5v/euupGaav7FLbiqJMLqoRFBB3iYSUsRq9dPXHSbiepNctqGVWRYjjfTF6IglCAR9vOm3RkOesKQvy8ZedSFnITyjg473nL6c0mGUacrV3LAn4uMu1yGez/UhXhhCAoRdmxzy05cBx2nqj7DjaTSyRYpftCH/g+eF7Cr3r1if4y3PNvNjRl2Eqy56/oiiTiwqCArK0ITMztjeaSLd8dBbbk+fXUFcRoiMco6s/PuqOXLlwVyy9dM3sQbkJbuLJweYcd99fN3d96BwA2vsGznfC5/7M5373LGCZqB7d2z6kQGi2M6J7IomCl6pQFKVwqCAoICfNy2yq0hdN0mYvyl985Rped+oC3rhxIbPKQ0TiVunlQgiCMjvf4PQldUNWQd3d3EMqZdIO5a+/7uT0NnffXzeO76C9N7MDmiNoAj7hLT98LB0N5MbtP9jV3MPxAvR0VhTFG9RHUEDWzs9slfjM4a70grhqTjWvONmKn6+rsBb//W191BfAcbp6TjXXX7GKN25cyA8f3kd3fwJjTNB69U8AAA3RSURBVDoC6KFdrbz9x5t45SnzePm6uQAsdJWymDWEIAgFrBpK7qJ4bvzDdARzt9f8l988A8AFJzbyjTeuH93NKYriOaoRFJD5tWWsmlPF6061Grt8+OdPpRO23JEyjilmf3u4IBqBzye87/zl1FWErFDSZIpIfGAh/u2ThwCr74CjEbj9AlUlQz8P9A1Xa2iYzpC5jlvWUDmk9qEoyuShgqCAiAh3X3cebz9rIJLmgedbCPl9GQ5d92JYCEHgxrmOYx463NnPn545BkDclWvglK9w5j0UqWEiRA+5iudl5zCEY4NDYmdr/oCiTElUEHhAhesJ+4n9x2moDGUstrO8FAS249jpjfDnZ44SS6Z4zYb5hOPJ9AJdiMidXc0DlVOzezHkqlo6N0e+gqIok48KAg9Y0VTJT991RroURHZ4Zp0rSqe6wILAESyORtAdSSACK2dXYgx02k7bsqAfnwxUGx0Kt1P5tRvmZ2zrd2kBnVmCIBwbLAjmjbEnsaIo3uJl8/qFIvKAiOwQke0i8pGs7Z8QESMiRVmI/pyVDSxrtMJJsxuuuBf/7LpB48U5d5e9MIejCcqD/rQfoL3PEgQlAR/bvnQZW7/4smHP98bTFqbLZ7zznKV88rITc+6XHR7aZ2dLu4WHagSKMjXxUiNIAB83xqwGzgQ+ICJrwBISwKXAix5ef9KZYzdjX5KVX+COthkqq3esVKf7IlhP5H2xJOUlgXRvg46+GKGAD59PqCwJpJPGhqM0aP2ZBP2+QSafS1Zb7SU7wzGiiST/9D+b2PRCR9pZ/J7zBkprz9aMYkWZkngmCIwxR40xT9rve4AdgPN4+E3gU0D+xWqmIc7NzR3GJDKnurBPyY1VJYjAgXbLkRuOJagI+dOF6tp7Y5SN0j/w5avWsqKpksX15Vx9xiLedqb1AvjwxVZ5jM7+OI/t6+CBna38avNB3v+zJwGoCAW46bXruGhVU0bTHUVRpg4TkkcgIkuADcDjIvIq4LAx5unholWKgRPscsvu0hPZFFojqCoNcuLsKjYf6ACsMM7y0IBG0N4XTT/h58tLlzfw14+dD1j1lP71qnXEEik+eskJhALWubrC8XR11V9vOZQ+trzEz5tPX8SbTx+6jIaiKJOL54JARCqB3wDXYZmLPgsMb5i2jrsWuBZg0aLpuYi897xlnLygZtg2jIWOGgLYuGQWdzx5mEQyRV80SUXJgEbQ0RcriIM6FPBRX1mCMQa/TzgejnHfjsGlJvIxPSmKMrl4qquLSBBLCPzMGPNbYDmwFHhaRPYDC4AnRWRO9rHGmJuNMRuNMRsbG6dnP9uA3zekELj2vGWcMLty2Bj+sXLakjr6YkmeP9ZjmYZcPoLj4fioTUPDISLUlgV5/IWOQd3OwHJKK4oytfEyakiAW4AdxphvABhjnjHGNBljlhhjlgCHgFONMce8msdU5TNXruYvHz3fk3NvXGK1fnxifwd9sSQVoQAVIVeF0gJX/6wpD7LlwHEA3npGpvZW7OY/RSkGvHxcOxu4BrhIRLbarys9vJ5iM7+2jNnVJTxzqMv2Efgpd3U1Ky3wU7rTRe2UhbXc8KqT+Pv1FxX0/IqieItnBlxjzCMMW40GbK1A8YCFs8o50tVPX9QyDbk1gkLb7Z1M6jOX1hH0+5hfW8a9Hz2PI3a3NkVRpjbqyStS5tSU8szhLsKxJOUhP6VBH2/auJDnjnbzzxeuKOi1nGSyE+cMNKVfObtKm9QryjRBBUGRMq+2LN2prKIkgIjwtdefPMJRY6O523rydwsCRVGmDxrSUaS4k9i8bhZ/sZ1dvLyx0tPrKIriDaoRFClzawaS2NYvqvX0Wje8ai0fveQE7UWsKNMU1QiKlDOX1aXfr/D4ST0U8NFUrZVFFWW6ohpBkVJbHuKHb99IW28U3wilphVFmdmoIChiLl0ze7KnoCjKNEBNQ4qiKDMcFQSKoigzHBUEiqIoMxwVBIqiKDMcFQSKoigzHBUEiqIoMxwVBIqiKDMcFQSKoigzHDHGTPYcRkREWoEDYzy8AWgr4HSmA3rPMwO955nBeO55sTFmxF6/00IQjAcR2WyM2TjZ85hI9J5nBnrPM4OJuGc1DSmKosxwVBAoiqLMcGaCILh5sicwCeg9zwz0nmcGnt9z0fsIFEVRlOGZCRqBoiiKMgxFLQhE5HIR2Skie0Tk+smeT6EQkR+LSIuIPOsaqxORe0Vkt/3vLHtcROTb9newTUROnbyZjw0RWSgiD4jIDhHZLiIfsceL+Z5LRWSTiDxt3/MN9vhSEXncvudfikjIHi+xP++xty+ZzPmPBxHxi8hTInKX/bmo71lE9ovIMyKyVUQ222MT+rddtIJARPzAd4ErgDXAW0RkzeTOqmD8BLg8a+x64D5jzErgPvszWPe/0n5dC3x/guZYSBLAx40xq4EzgQ/Y/5fFfM9R4CJjzCnAeuByETkT+BrwTfuejwPvsvd/F3DcGLMC+Ka933TlI8AO1+eZcM8XGmPWu8JEJ/Zv2xhTlC/gLOAe1+dPA5+e7HkV8P6WAM+6Pu8E5trv5wI77ff/Dbwl137T9QXcCVw6U+4ZKAeeBM7ASiwK2OPpv3HgHuAs+33A3k8me+5juNcFWAvfRcBdgMyAe94PNGSNTejfdtFqBMB84KDr8yF7rFiZbYw5CmD/22SPF9X3YKv/G4DHKfJ7tk0kW4EW4F5gL9BpjEnYu7jvK33P9vYuoH5iZ1wQvgV8CkjZn+sp/ns2wF9EZIuIXGuPTejfdjH3LM7VsX0mhkgVzfcgIpXAb4DrjDHdIrluzdo1x9i0u2djTBJYLyK1wB3A6ly72f9O+3sWkVcALcaYLSJygTOcY9eiuWebs40xR0SkCbhXRJ4fZl9P7rmYNYJDwELX5wXAkUmay0TQLCJzAex/W+zxovgeRCSIJQR+Zoz5rT1c1PfsYIzpBB7E8o/UiojzAOe+r/Q929trgI6Jnem4ORt4lYjsB36BZR76FsV9zxhjjtj/tmAJ/NOZ4L/tYhYETwAr7YiDEPBm4PeTPCcv+T3wDvv9O7Ds6M742+1ogzOBLkflnC6I9eh/C7DDGPMN16ZivudGWxNARMqAS7AcqA8Ar7d3y75n57t4PXC/sY3I0wVjzKeNMQuMMUuwfq/3G2OupojvWUQqRKTKeQ+8DHiWif7bnmxHicdOmCuBXVi21c9O9nwKeF8/B44CcawnhHdh2UbvA3bb/9bZ+wpW9NRe4Blg42TPfwz3ew6W+rsN2Gq/rizyez4ZeMq+52eBL9jjy4BNwB7gdqDEHi+1P++xty+b7HsY5/1fANxV7Pds39vT9mu7s05N9N+2ZhYriqLMcIrZNKQoiqLkgQoCRVGUGY4KAkVRlBmOCgJFUZQZjgoCRVGUGY4KAmXSEZGkXXnReV1vjz8oIhPen1ZEfiIir88a+649t+dEpN8119eLyI0icokH8xARuV9EqkdxzKtkhEq7do7C3eOfoVIsFHOJCWX60G+MWT/ZkxgOY8wHIF3r6K6s+f7ao8teCTxtjOnO9wBjzO8ZIXHSGNMqIkdF5GxjzN/HO0ll+qMagTItEJHvi8hmcdXmt8f3i8jXxKrdv0lEVtjjbxCRZ8Wq5/+QPeaX/7+9cwuxMYri+O8vhRKlJKTIXZmEGSFEjFxyKbk/iCY8eOOFmuIBNUU0L+JBSsqTF2UUZTQmuQwmQi4PygNKbqFkeVj7M5/TYJiZnHHWr07f9+2zv3XWPg/f2nuds/9LqpF0LWm5b07tklSbZvtnaRH4aqtv31cQyZ+9khqTvxMl1Ul6LGlL7p4dOT92/8T0OtKOUklDJd2XdCyN66SkuZIa5Jr1FanfBkm1Ob8OS7oi6UnBKudMsh8EEQiCoqBXQWpoVSt9dplrtZcBsySV5d57a2YVQC2uTQNQDcw31/Nfkto24Vvyy4FyoErSMGA5MBoYD1QB09o5nmdmNhW4jNeOWIHrBO0BkFSJ68lX4LUGJkma2Yqd6cCN3PUI4BD+HYwB1uK7rrcDO3/iy8DUZzGwP9d+HZjx50ML/kciNRQUA21JDa2US/R2xx9u43D5BXDJjex4MJ03AMclnQYykbpKoCw3M+6LP5BnAqfM1T6fS7rYzvFkqZlmoLeZvQPeSfqU9IMq06sp9eud/KgvsNMv3Zvx1MyaASTdxQuXmKRmvD5Fa5wxs6/APUkDcu0vgEF/N7zgfyMCQVD0pFn7dqDczF5LOo7rzGRY4bmZbZE0BVgE3JI0Addp2WZmdQX2F9Kx8sWf0/Fr7jy77p782GdmR35j54ukbulBnrdbaDuz+ytf4EcJ457Ax998flAiRGoo6Ar0AT4Ab9KsdkHB+6tyx0YAScPN7KqZVeOVq4bgFa22yiWtkTQqKT7WA6vTbwgDgdmdPJ46YKO8vgKSBsu16At5gIuSdQajcDG7IIgVQVAU9JJX4so4Z2bf/wJpZrclNeHqjE/wtE+eHpKu4hObNamtRtJIfBZ8AVd3vIOnUG5KEvASWIZrwM/BUzkPgUsdO7wfMbPzksYCje4G74H1tGjOZ5zFVTgfdYIbs5P9IAj10aBrIy9iMtnMXv1rXzqatDo5YWbzOsF2PbDUzF53tO2g6xGpoSAoUswLjhz9kw1lbUFSf+BABIEgI1YEQRAEJU6sCIIgCEqcCARBEAQlTgSCIAiCEicCQRAEQYkTgSAIgqDEiUAQBEFQ4nwD5f7d9sud7DMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ys = [30]\n",
    "xs = range(0,501)\n",
    "np.random.seed(seed=42)\n",
    "for delta in np.random.normal(0,0.5,500):\n",
    "    ys.append(ys[-1] + delta)\n",
    "    \n",
    "plt.plot(ys)\n",
    "plt.ylabel('Stock Price ($)')\n",
    "plt.xlabel('Elapsed Time (min)')\n",
    "plt.savefig('figures/1.01.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = stats.linregress(xs,ys)\n",
    "line =  [r.slope * x + r.intercept for x in xs]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "std = np.std([(y-y0) for y,y0 in zip(ys,line)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "top = [y + std for y in line]\n",
    "bottom = [y - std for y in line]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xs,ys)\n",
    "plt.plot(xs,line)\n",
    "plt.plot(xs,top)\n",
    "plt.plot(xs,bottom)\n",
    "plt.ylabel('Stock Price ($)')\n",
    "plt.xlabel('Elapsed Time (min)')\n",
    "plt.savefig('figures/1.02.svg')\n",
    "plt.savefig('figures/1.03.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1.2 Finding a good deal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "mileages = [4.1429, 8.9173, 6.5, 6.0601, 12.3, 6.2, 2.5782, 0.9, 1.7, 13.1045, 24.7, 9.2699, 17.2, 10.0, 10.0, 2.8, 12.3773, 19.6, 7.3397, 2.1178, 12.9886, 10.9884, 16.9, 6.0, 12.9, 8.1936, 10.5, 8.0713, 1.7, 10.0, 15.6097, 17.0, 16.7, 5.6, 11.3, 19.9, 9.6, 21.6, 20.3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "prices = [16980.0, 15973.0, 9900.0, 15998.0, 3900.0, 12540.0, 21688.0, 17086.0, 23000.0, 8900.0, 3875.0, 10500.0, 3500.0, 26992.0, 17249.0, 19627.0, 9450.0, 3000.0, 14999.0, 24990.0, 7967.0, 7257.0, 4799.0, 13982.0, 5299.0, 14310.0, 7800.0, 12250.0, 23000.0, 14686.0, 7495.0, 4950.0, 3500.0, 11999.0, 9600.0, 1999.0, 4300.0, 3500.0, 4200.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def price(mileage): \n",
    "    return 26500 * (0.905 ** mileage)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.linspace(0,25,100)\n",
    "ys = [price(x) for x in xs]\n",
    "\n",
    "plt.scatter(mileages,prices) \n",
    "plt.plot(xs,ys, color='C1')\n",
    "plt.xlabel('Mileage (10,000s of miles)')\n",
    "plt.ylabel('Price ($)')\n",
    "plt.savefig('fig1.5.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.linspace(0,25,100)\n",
    "ys = [price(mileage) for mileage in xs]\n",
    "\n",
    "\n",
    "target_mileage = log(10/26.5)/log(0.905)\n",
    "\n",
    "plt.scatter(mileages,prices) \n",
    "plt.plot(xs,ys, color='C1')\n",
    "\n",
    "xlim,ylim = plt.xlim(), plt.ylim()\n",
    "\n",
    "plt.plot([-5,30],[10000,10000],color=\"gray\",linestyle=\"dashed\")\n",
    "plt.plot([target_mileage,target_mileage],[-5000,10000],color=\"gray\",linestyle=\"dashed\")\n",
    "plt.xlim(*xlim)\n",
    "plt.ylim(*ylim)\n",
    "plt.xlabel('Mileage (10,000s of miles)')\n",
    "plt.ylabel('Price ($)')\n",
    "plt.savefig('fig1.6.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6070757653156251"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.905 ** 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1.3 Building 3D graphics and animations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import sys\n",
    "sys.path.append('../Chapter 03')\n",
    "from draw3d import *\n",
    "\n",
    "triangle = [(2.3,1.1,0.9), (4.5,3.3,2.0), (1.0,3.5,3.9)]\n",
    "\n",
    "draw3d(\n",
    "    Polygon3D(*triangle),\n",
    "    Points3D(*triangle),\n",
    "    axes=False,\n",
    "    origin=False\n",
    ")\n",
    "plt.savefig('figures/1.08.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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